Need help with basic file security

First off, I posted once before but I'm afraid I was a little too vague and perhaps rushing a bit so I'm creating a new post with a simple question:
Can someone provide a well documented example of a secure method of writing files that's platform independent (java 1.7 preferred). In short I want to create a program that can be used on any platform (eventually I'll port it from PC to Mobile) that can read and write secure files to a local directory. I do not want to write any files to the internet nor do I want anything specific to one system, the encryption needs to be completely within Java.

I've honestly never done secure I/O of any sort before and I've just started working with java.nio so I don't know much except that it saved me a heck of a lot of coding in my iTunes playlist transfer program. I do know that I'll need some way of backing up the encryption and that I want to use password protection.

The program I wish to create is a banking app, the code of which will center somewhat around the security method (So I don't even have much pseudo code yet). I came up with the idea a while back but my old laptop fried on me so I wasn't able to focus any time on it until now. For those interested my hope for the end app (and this will take quite some time) is that it will be able to: keep a checkbook, keep a weekly and a monthly cash flow chart ($22/week on lunch&drink, $15/week me-cash(or blow money), gas, maintenance, ect), include a unique and simple math language for calculating cash flow charts. For my first task I'll be working on the unique and simple math language.

iTunes Playlist Transfer Program: reads an exported iTunes Playlist XML and ask user for XML location and Device Music Directory, it then [in short] transfer music to the device/deletes music not wanted on device.